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Математичні моделі процесу управління декомпресією та їх аналіз: Автореф. дис… канд. фіз.-мат. наук / Г.Ю. Онопчук, НАН України. Ін-т кібернетики ім

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Iaoe?iiaeueia aeaaeai?y iaoe Oe?a?ie

?inoeooo e?aa?iaoeee ?iai? A.I.Aeooeiaa

IIII*OE Aaeeia TH???aia

OAeE 519.876

IAOAIAOE*I? IIAeAE? I?IOeANO OI?AAE?IIss

AeAEIII?AN??TH OA ?O AIAE?C

01.05.02 – iaoaiaoe/ia iiaeaethaaiiy oa ia/enethaaeuei? iaoiaee

Aaoi?aoa?ao aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe

Ee?a 1999

Aeena?oaoe??th ? ?oeiien.

?iaioo aeeiiaii a ?inoeooo? e?aa?iaoeee ?iai? A.I.Aeooeiaa IAI Oe?a?ie

Iaoeiaee ea??aiee: aeieoi? o?ceei-iaoaiaoe/ieo iaoe

IIEIOEEI A’y/aneaa A?eai?iae/,

?inoeooo ee?oeiii? a?ieia?? oa aaiii? ?iaeaia???

IAI Oe?a?ie, canooiiee aee?aeoi?a

Io?oe?ei? iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe,

noa?oee iaoeiaee ni?a?ia?oiee

IAI?I A?eoi? Ieoaeeiae/,

?inoeooo i?eeeaaeiiai nenoaiiiai aiae?co

IAI Oe?a?ie oa I?iina?oe,

i?ia?aeiee iaoeiaee ni?a?ia?oiee;

eaiaeeaeao o?ceei-iaoaiaoe/ieo iaoe, aeioeaio

IAOA??IEI Aieiaeeie? Oeoiiiae/,

Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea,

aeioeaio.

I?ia?aeia onoaiiaa: ?inoeooo eini?/ieo aeine?aeaeaiue IAI Oe?a?ie

oa Iaoe?iiaeueiiai eini?/iiai aaaionoaa Oe?a?ie,

a?aeae?e eini?/ieo ?ioi?iaoe?eieo oaoiieia?e oa nenoai.

Caoeno a?aeaoaeaoueny “25” /a?aiy 1999 ?. i 11 aiae.

ia can?aeaii? niaoe?ae?ciaaii? a/aii? ?aaee Ae 26.194.02 i?e ?inoeooo?
e?aa?iaoeee ?iai? A.I.Aeooeiaa IAI Oe?a?ie

ca aae?anith: 252022 Ee?a 22, i?iniaeo Aeaaeai?ea Aeooeiaa,40.

C aeena?oaoe??th iiaeia iciaeiieoenue o iaoeiai-oaoi?/iiio a?o?a?
?inoeoooo.

Aaoi?aoa?ao ?ic?neaiee “13” o?aaiy 1999 ?.

O/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee NEIssANUeEEE A.O.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Caaea/? oi?aae?iiy, ui aeieeathoue i?e i?aai?caoe??
oa i?iaaaeaii? aaa??eii-?yooaaeueieo, ?yooaaeueieo,
i?aeaiaeii-oaoi?/ieo, noaeiaeo oa noaei?aiiioieo aiaeieacieo ?ia?o
ciaoiaeyoueny a cii? iino?eii? oaaae iaoeiaoe?a oa aeine?aeiee?a. Aiie
iia’ycai? ?c iaiao?aei?noth aa?aiooaaiiy aaciaee aiaeieacieo nione?a i?e
?yooaaii? ethaeae, aaa??eieo noaeai; aoae?aieoeoa? oa ?aiiio?
a?ae?ioaoi?/ieo nii?oae; i?ieeaaeaii? i?aeaiaeieo eiioi?eaoe?e; i/enieo
?ia?o aiaeieo oeyo?a, eaiae?a, aeaaoi??e; aenieoaoaoe?? ii?nueeeo oa
ieaai?/ieo ?ano?n?a oiui.

?iaioa i?enay/aia iiaoaeia? iaoaiaoe/ieo iiaeaeae i?ioeano oi?aae?iiy
aeaeiii?an??th – aacia/iiai ia?aaiaeo noaio i?aai?cio, ui ia?aaoaaa i?ae
ae??th a?ia?aa??? (i?aeaeuaiiai a?ae?inoaoe/iiai oeneo), aei
ii?iiaa?e/ieo oiia. I?e aeaeiii?an?? aa?iiao?e/iee oene, i?ae yeei
iiaea?oueny aeeoaeueia noi?o aeaaiaaoo, iaaea? i?iii?oe?eii oaeaeeino?
i?aeeiio ? iai?aaeeueiee ?? aea?? iiaea i?ecaanoe aei eaniiii? oai?iae.
Oiio caaea/a aeai?o oaeaeeino? aeaeiii?an?? aeaaiaaoa ? i?aai?caoe??
i?ioeano aeaeiii?an?? ? aeooaeueiith ? iaei??th ?c aieiaieo i?e
ieaioaaii? oa i?iaaaeaii? i?aeaiaeieo ?ia?o.

Aeei?enoaiiy iaoaiaoe/ieo iiaeaeae aeey oi?aae?iiy aeaeiii?an??th
?icii/aoi ?iaioaie Aeae.Oieaeaeia (1906 ?.). I?ioyaii noie?ooy oeth
i?iaeaio aeine?aeaeoaaee a?o/eciyi? oa ca?oa?aei? a/ai? A.I.Aaa?’yiia,
?.I.Aiaaoe?ueia, I.A.Aiiaea?aiei, I.I.Aooa??i, N.I.Aoey?,
I.I.A?aiaiaoeueeee, A.E.Caeueoeiai, Ae.?.Ia?/aiei, A.A.I?nth?a,
A.I.I?eiea?a, Aeae.Aiiae, ?.Ae.Aaii, I.?.Iaoaee, E.Aeae.Eaiaa?noai,
?.A.Oaiieiai, I.Ae.ss?a?i oa ?i.

Iia? aenia?eiaioaeuei? aeai?, ?acoeueoaoe iaoeiaeo aeine?aeaeaiue,
?icaeoie oai??? iioeiaeueieo ??oaiue oa iaoaiaoe/iiai iiaeaethaaiiy
aeathoue iiaeeea?noue ooi/ithaaoe, aaeineiiaethaaoe ? noai?thaaoe iia?
iaoaiaoe/i? iiaeae? oi?aae?iiy aeaeiii?an??th.

Iaoa ?iaioe iieyaa? o ?ic?iaoe? iaoaiaoe/ieo iiaeaeae oi?aae?iiy
aeaeiii?an??th, iioeiaeueiiai uiaei oaeaeeiae?? ca ?aooiie aeai?o
oi?aaeyth/eo ia?aiao??a – neeaaeo aeeoaeueii? noi?o? oa oaeaeeino?
i?aeeiio, ia?aiao?aie naiii?aai?caoe?? nenoaie ianiia?aiino aac?a
aeiionoeieie iaaaioaaeaiiyie ia noiyieao o?a?eoi???; ?o iaoaiaoe/iiio
iaa?oiooaaii? oa /enaeueiiio aiae?c?.

Aeey aeinyaiaiiy aeacaii? iaoe a ?iaio? noi?ioeueiaai? oa ?ica’ycai?
oae? caaea/?:

1. Iiaoaeoaaoe iaoaiaoe/i? iiaeae? i?ioean?a ianiia?aiino aac?a a
nenoai? e?ia – oeaieii? ?aca?aoa?e oa i?iaanoe ?o iaoaiaoe/iee aiae?c.

2. Oi?iae?coaaoe nenoaio iaiaaeaiue ia i?ioean i?iaaaeaiiy i?aeaiaeieo
caio?aiue.

3. Iinoaaeoe ? iaa?oiooaaoe caaea/o iioeiaeueiiai uiaei oaeaeeiae??
oi?aae?iiy aeaeiii?an??th ca ?aooiie aeai?o neeaaeo aeeoaeueii? noi?o?
oa oaeaeeino? i?aeeiio, oa oi?aae?iiy ia?aiao?aie naiii?aai?caoe??
nenoaie aeiionoeieie iaaaioaaeaiiyie ia noiyieao o?a?eoi???.

4. ?ic?iaeoe aeai?eoie oi?aae?iiy i?ioeanii caio?aiiy – eiii?an??,
aeniiceoe?? ia aeeaei? oa iioeiaeueiiai oi?aae?iiy uiaei oaeaeeiae??
i?ioeanii aeaeiii?an?? ia ae?eyieao o?a?eoi??? i?ae /an noiyiie oa
i?aeeii?a.

5. Io?eiaoe ioe?iee o?eaaeino? aoai?a i?aeeiio ? noiyiie i?e
aeaeiii?an??.

6. ?ic?iaeoe i?ia?aiia caaacia/aiiy i?ioeano oi?aae?iiy aeaeiii?an??th
oa i?iaanoe aiae?c ?acoeueoao?a ia/enethaaeueieo aenia?eiaio?a c
iiaeaeyie.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aeena?oaoe?y
aeeiioaaeanue ca?aeii c ieaiii iaoeiaeo aeine?aeaeaiue a ?aieao
athaeaeaoii? iaoeiai-aeine?aeii? oaie ?inoeoooo e?aa?iaoeee ?iai?
A.I.Aeooeiaa IAI Oe?a?ie “sse?niee aiae?c ? iioei?caoe?y eiioe?eoii
ea?iaaieo i?ioean?a” (oeo? aea?aeaaii? ?a?no?aoe?? 0198U003464).

Iaoeiaa iiaecia. Iiaoaeiaaii iaoaiaoe/io iiaeaeue iioeiaeueiiai uiaei
oaeaeeiae?? i?iaaaeaiiy aeaeiii?an??. Iieacaii aaeaeaaoi?noue
iaoaiaoe/ieo ia’?eo?a oi?aae?iiy – aeeiai?/ieo nenoai o?ainii?oo ?
ianiiai?io aac?a a i?aai?ci? (aeiaaaeaii iaiaaeai?noue ?o ?ica’yce?a,
aneiioioe/io no?ee?noue oa ea?iaai?noue). Iaea?aeai? ioe?iee o?eaaeino?
aoai?a i?aeeiio oa noiyiie ia o?a?eoi??yo ?ooo, aea aa?aioiaaia aaciaea
i?ioeano aeaeiii?an??. Iieacaii iiaeeea?noue i?enei?aiiy i?ioeano
aeaeiii?an?? i?e aeeaieiaiaeieo caio?aiiyo oeyoii oi?aae?iiy ia?aiao?aie
naiii?aai?caoe?? nenoaie ca ?aooiie aeei?enoaiiy aeiionoeieo
iaaaioaaeaiue ia noiyieao. ?ic?iaeaii /enaeuei? aeai?eoie iioeiaeueiiai
oi?aae?iiy aeaeiii?an??th.

Iaoiaee aeine?aeaeaiue. I?e ?ic?iaoe? iiaeaeae ? ?o aeine?aeaeaii?
aeei?enoaii oai??th cae/aeieo aeeoa?aioe?eieo ??aiyiue, oai??th
iioeiaeueiiai oi?aae?iiy, iaoiaee iaoaiaoe/iiai iiaeaethaaiiy oa iaoiaee
ia/eneaiue.

I?aeoe/ia oe?ii?noue. Cai?iiiiiaaiee iaoiae i?iaaaeaiiy aeaeiii?an??
aeicaiey? cia/ii nei?ioeoe ?? /an ca ?aooiie aeai?o iioeiaeueieo
oi?aaeyth/eo ia?aiao??a, ? oiio iiaea aeei?enoiaoaaoenue a i?ia?aiiiio
caaacia/aii? aaoiiaoeciaaiiai ?iai/iai i?noey ea??aieea i?aeaiaeieo
?ia?o.

Aeinoia??i?noue iaoeiaeo iieiaeaiue, aeniiae?a ? i?aeoe/ieo
?aeiiaiaeaoe?e, ui i?noyoueny a aeena?oaoe??, i?aeoaa?aeaeo?oueny
iaoeiaith iaa?oioiaai?noth iiaeaeae oa ?acoeueoaoaie ia/enethaaeueieo
aenia?eiaio?a.

Ai?iaaoe?y ?iaioe. Iniiai? ?acoeueoaoe aeena?oaoe?eii? ?iaioe
aeiiia?aeaeenue oa iaaiai?thaaeenue ia I?aeia?iaei?e eiioa?aioe??
“Ieoaiiy iioei?caoe?? ia/eneaiue” (Ee?a,1997), I?aeia?iaei?e
eiioa?aioe?? “A?iien?y: eiino?oeoeaia oa aeano?oeoeaia ae?y”
(Ee?a,1998), iaoeiaeo nai?ia?ao ?inoeoooo e?aa?iaoeee ?iai? A.I.Aeooeiaa
IAI Oe?a?ie (1997-1999).

Ioae?eaoe??. Ca iaoa??aeaie aeena?oaoe?? iioae?eiaaii o?noue iaoeiaeo
i?aoeue, a oiio /ene? /ioe?e – a oe?a?inueeeo iaoeiaeo aeo?iaeao oa
ca??ieeao, aea? a iaoa??aeao oa oacao eiioa?aioe?e.

Iniaenoee aianie aeena?oaioa a ?iaioao, aeeiiaieo o ni?aaaoi?noa?,
iieyaa? a iinoaiiaoe? iaoaiaoe/ieo caaea/, iiaoaeia? iaoaiaoe/ieo
iiaeaeae ia’?eoo oi?aae?iiy, ?ic?iaoe? /enaeueieo aeai?eoi?a oa
i?ia?aiiiai caaacia/aiiy, ?ioa?i?aoaoe?? ?acoeueoao?a ia/enethaaeueieo
aenia?eiaio?a.

No?oeoo?a oa ianya ?iaioe. Aeena?oaoe?eia ?iaioa neeaaea?oueny c anooio,
o?ueio ?icae?e?a, aeniiae?a oa nieneo aeei?enoaieo aeaea?ae c 122
iaeiaioaaiue. Caaaeueiee ianya ?iaioe neeaaea? 119 noi??iie. Oaeno
aeena?oaoe?? i?noeoue 14 ?enoie?a oa 2 oaaeeoe?.

INIIAIEE CI?NO ?IAIOE

O anooi? noi?ioeueiaaii iaoo aeena?oaoe?eii? ?iaioe, iaa?oioiaaii ??
aeooaeuei?noue, iaoeiao iiaecio oa i?aeoe/ia cia/aiiy, ei?ioei
aeeeaaeaii ci?no ?iaioe.

Ia?oee ?icae?e i?noeoue aiae?c noaio i?iaeaie aeaeiii?an?? oa
iinoaiiaeo, ia ci?noiaiiio ??ai?, caaea/ uiaei i?aeo?eiaiiy ?? aaciaee.
A iaeyae? ?ia?o iniiaia oaaaa i?eae?ey?oueny i?iaeaiai, ui iia’ycai? c
iiaoaeiaith iaoaiaoe/ieo iiaeaeae oi?aae?iiy ianiiai?iii aac?a a
i?aai?ci? ethaeeie i?e a?ia?aa??? oa no/aniei iaoaiaoe/iei iaoiaeai, ui
aeei?enoiaothoueny aeey ?ic?aooie?a ?aaeei?a aacia/ii? aeaeiii?an??. I?e
iiaoaeia? iaoaiaoe/ieo iiaeaeae eiii?an?? oa aeaeiii?an??
oi?iae?cothoueny, o aeaeyae? nenoaie iaiaaeaiue ia i?iaaaeaiiy oeeo
i?ioean?a, aenia?eiaioaeueii anoaiiaeai? i?iyae iaaaoeaiiai aieeao
a?ia?aa??? ia i?aai?ci, ? ?aaeaiaioothoue iiiaeeio aeiionoeieo ??oaiue
uiaei eiio?ieth oa oi?aae?iiy i?ioeanaie. Na?aae oaeoi??a, ye? iniaeeai
iaiao?aeii a?aoiaoaaoe i?e i?aai?caoe?? ?ia?o ia aeeaei? oa i?e
aeaeiii?an??, aeae?eythoue ia?aiaee neiae?ii aenieeo oene?a, acioiee
ia?eic, eeniaaa io?o?iiy i?aai?cio oa eaniiio oai?iao.

Ae?oaee ?icae?e i?enay/aiee iiaoaeia? iaoaiaoe/ieo iiaeaeae oi?aae?iiy
aeaeiii?an??th oa ?o ye?niiio aiae?co. Oaeiae i?noyoueny iniiai?
?acoeueoaoe aeine?aeaeaiue.

Aeoiaey/e c oiai, ui aaciaea i?aai?cio i?e eiii?an?? ? aeaeiii?an??
iia’ycaia c i?iaeaiith oaeaeeiai iane/aiiy ? ?icne/aiiy oeaiei a?ae
?ia?oieo aac?a, c iiaeeea?noth ooai?aiiy aaciaeo aiaie a e?ia? ?
oeaieiao, a iniiao aeine?aeaeaiiy i?iaeaie aacia/ii? aeaeiii?an??
iieeaaeai? iaoaiaoe/i? iiaeae? o?ainii?oo oa ianiiai?io ?ia?oieo aac?a
(i?ae?icae?e 2.1 oa 2.2). Oaciaeie ci?iieie, ui oa?aeoa?ecothoue noai
nenoaie ianiiai?io aac?a, ? ia?oe?aeuei? oenee (iai?oaeaiiy) aac?a o
aeueaaieao, e?ia? ? oeaieiao.

I?e ?ic?iaoe? iaoaiaoe/ieo iiaeaeae i?eeiyoi, ui

aeaea?aeii ?ia?oiiai aaco aeey oeaiei ? e?ia, ui iieaa? oeaieio ;

a e?ia? ?ia?oi? aace ciaoiaeyoueny a ?ic/eiaiiio aeaeyae?;

iaoai?ciii ?iciianthaeaeaiiy aaco ? a?eueia aeeooc?y a oeaieiao oa
i?iieeiaiiy eiai /a?ac aa?’??e, ui ?icae?eythoue e?ia ? oeaieio, a
oaeiae i?eioniaa oee?eoeyoe?y (o?ainii?o aaco e?ia’th a ?ic/eiaiiio
aeae?).

O ?iaio? oaeiae i?eionea?oueny, ui iai?oaeaiiy ?ia?oiiai aaco a
a?oa??aeuei?e e?ia? aei??aith? a?aeiia?aeiiio ia?oe?aeueiiio oeneo aaco
a aeeoaeuei?e noi?o?.

caaaeueiee oene aeeoaeueii? noi?o?

, (1)

– ia?aa?aeiee eiao?oe??io.

? noiith ia?oe?aeueieo oene?a eiaeiiai ie?aiiai aaco. Ioaea

, (2)

– ia?oe?aeueiee oene aae?th; oene aoaeaeeneiai aaco ? aiaeyieo ia??a o
iiaeae? ia a?aoiao?oueny.

ia aoaeue-ye?e aeeaei?, oi

, (3)

, (4)

aecia/athoueny ni?aa?aeiioaiiyie:

. (5)

oa a?aae??io iai?oaeaiue ?ia?oieo aac?a o e?ia? ? oeaiei?
caaacia/othoue oi?ioaaiiy iioie?a aaco /a?ac no?ieo eai?ey??a

, (6)

– iai?oaeaiiy ?ia?oieo aac?a o oeaieii?e ??aeei?, m – e?euee?noue
?icaeyaeoaaieo oeaieiieo ?aca?aoa??a.

) iieno?oueny nenoaiith aeeoa?aioe?eieo ??aiyiue:

, (7)

, (8)

, (9)

, (10)

– eiao?oe??ioe ?ic/eiiino? acioo ? aae?th o e?ia? ? oeaieii?e ??aeei?
a?aeiia?aeii.

Ci?io iai?oaeaiue ?ia?oiiai aaco a a?oa??aeuei?e e?ia? iiaeia
i?aaenoaaeoe ??aiyiiyie

(11)

, (12)

) – /an ia?aaoaaiiy i?ae aieeaii a?ia?aa?e/ieo oiia.

– caaeaia aeeaeia caio?aiiy.

I?e iiaeaethaaii? i?ioeano ianiiai?io aac?a o i?aai?ci? i?e a?ia?aa???
aeae?eythoue oeaieii? ?aca?aoa?e, ye? nooo?ai a?ae??ciythoueny
eiao?oe??ioaie ?ic/eiiino? aac?a. I?e iino?eieo eiao?oe??ioao o i?aaeo
/anoeiao ??aiyiue (7)-(10) nenoaia ??aiyiue ? e?i?eiith c iao?eoeath,
yea ia? aei/ii – ae?aaiiaeueio no?oeoo?o.

O i?ae?icae?e? 2.3 aeine?aeaeo?oueny nenoaia, ui iieno? ianiiai?i
?ia?oieo aac?a o i?aai?ci? i?e a?ia?aa???.

Iaoae

(13) ii/aoeia? oiiae aeey nenoaie (7)-(12). O a?aeiia?aeiino? c
a?aeiieie oai?aiaie oai??? aeeoa?aioe?eieo ??aiyiue nenoaia (7)-(12) ia?
?aeeiee ?ica’ycie, yeee iaia?a?aii caeaaeeoue a?ae ii/aoeiaeo oiia oa
ia?aiao??a, ui aoiaeyoue aei i?aaeo /anoei ??aiyiue nenoaie. Oaeiae
ni?aaaaeeeaa

Oaa?aeaeaiiy 1. ?ica’ycie nenoaie (7)-(12) iaa?ae’?iiee i?e iaa?ae’?iieo
ii/aoeiaeo oiiaao oa iaiaaeaiee caa?oo.

Oe? iieiaeaiiy neeaaeathoue iaoaiaoe/ia iaa?oiooaaiiy ia?aii? aeey
aiae?co iiaeae? ianiiai?io ?ia?oieo aac?a o i?aai?ci? i?e a?ia?aa???.

?ica’ycee nenoaie (7)-(10) iiaeia aeienaoe o yaiiio aeaeyae?
(i?ae?icae?e 2.4).

??oaiiy nenoaie ??aiyiue (7)-(10) caiaeeoueny aei ?ica’yceo nenoaie
iacaeaaeieo ??aiyiue ae?oaiai ii?yaeeo c iino?eieie eiao?oe??ioaie

, (14)

, (15)

– ?ica’ycie nenoaie (11)-(12).

a?aeiia?aeieo oa?aeoa?enoe/ieo ??aiyiue ae?eni?, ??ci? ? a?ae’?ii?.
A?aeiia?aeii ni?aaaaeeeaa

Oaa?aeaeaiiy 2. Nenoaia iaeii??aeieo aeeoa?aioe?eieo ??aiyiue, ui
a?aeiia?aeathoue (7)-(10), aneiioioe/ii no?eea ca Eyioiiaei.

O i?ae?icae?e? 2.5 i?iaiaeeoueny nenoaiiee aiae?c iniaeeainoae ??cieo
oac ia?aaoaaiiy aeaaiaaoa i?ae a?ae?inoaoe/iei oeneii: i?e caio?aii?
(eiii?an?y), i?e ?iaio? ia aeeaei? (aeniiceoe?y ia a?oio?) oa i?e
i?aeeii? ia iiaa?oith ii?y (aeaeiii?an?y), ye? iaiao?aeii a?aoiaoaaoe
i?e iaoaiaoe/i?e iinoaiiaoe? caaea/? oi?aae?iiy i?ioeanii ia?aaoaaiiy
aeaaiaaoa ia aeeaei?. Iieacaii, ui, ye i?aaeei, ia noaae?? eiii?an?? ?
aeniiceoe?? ia a?oio? eaea iane/aiiy oeaiei ?ia?oieie aacaie, i?e
aeaeiii?an?? ie?ai? oeaieie iiaeooue aeiiane/oaaoenue, ?io? –
ciaoiaeeoenue a noaae?? ?icne/aiiy.

c eii?aeeiaoaie

, (16)

, yea a?aeiia?aea? aa?iiao?e/iiio oeneo ia iiaa?oi? ii?y, c
eii?aeeiaoaie

;

, (17)

.

Icia/aiiy 1. Aacia/iith iaceaa?oueny o?a?eoi??y ?ooo aeeiai?/ii?
nenoaie, i?e yeiio

, (18)

– aeiaeaoi? eiinoaioe.

E?eoa??e aaciaee i?ioeano aeaeiii?an?? aaco?oueny ia e?eoe/iiio
a?aeiioaii? iioieo ?ic/eiaiiai ?ia?oiiai aaco, ui aeoiaeeoue ?c
oeaieiiiai ?aca?aoa?o a e?ia, aei iioieo a?aeiia?aeiiai aaco a e?ia?
eai?ey?iiai ?onea. I?eeiyoee a aeena?oaoe?eiiio aeine?aeaeaii? e?eoa??e
aaciaee a?ae??ciy?oueny a?ae e?eoa??th Oieaeaeia (e?eoe/ia
ia?aiane/aiiy) oa eiai aeayeeo iiaeeo?eaoe?e (e?eoe/ia ??cieoey oene?a
aac?a). A?i a?aoiao? ia o?eueee nooi?iue iane/aiiy oeaieiiiai ?aca?aoa?o
?ia?oieie aacaie, aea ? iniaeeaino? i?ioean?a aeeooc??, ia?ooc?? oa
?ic/eiaiiy aaco a oeaieii?e ??aeei?.

Oiiae (20) caaeathoue oacia? iaiaaeaiiy ia o?a?eoi??? ?ooo nenoaie.

, ye? aeae?athoueny ?c aeiionoeieo iiiaeei

, (19)

. (20)

) ?c aeiionoeieo iiiaeei (19), (20) iaceaathoueny iioeiaeueieie, yeui
caaacia/othoue ia?aaaaeaiiy aeeiai?/ii? nenoaie (7)-(12) ?c oi/ee (16) a
oi/eo (17), i?e aeeiiaii? oaciaeo iaiaaeaiue (18) i?ae /an ?ooo, ca
i?i?iaeueiee /an.

O oae?e iinoaiiaoe? caaea/a oi?aae?iiy aeaeiii?an??th oi?ioeth?oueny ?
?ica’yco?oueny aia?oa. ??oaiiy oe??? caaea/? ciaoiaeeoueny aeey
aeiaaeeo, eiee aeaeiii?an?y ? nooi?i/aoith.

).

ii acioo ? aae?th a?aeiia?aeii

, (21)

, (22)

– ii/aoeiaee iiiaio i?aeeiio, a

. (23)

) cae?enith?oueny a iiiaio ii?ooaiiy oi/a a iaei??? c ia??aiinoae (18),
? o?eaa? aeioe, aeiee aeey an?o oeaieiieo ?aca?aoa??a iaeii/anii ia
aeeiiathoueny ia??aiino?

, (24)

– iaia?aae caaeai? aaee/eie.

O?eaae?noue noiyiie aecia/a?oueny ni?aa?aeiioaiiyi

(25)

aea

.

Ioe?iee o?eaaeino? oac i?aeeiio (21)-(23) ? noiyiie (25) aeicaieythoue
anoaiiaeoe ni?aaaaeeea?noue

), a iiiaeeiao (19), (20) ye? ia?aaiaeyoue aeeiai?/io nenoaio (7)-(12)
?c oi/ee (16) a oi/eo (17) i?e iaiaaeaiiyo (18).

Aeiaaaeaiiy oaa?aeaeaiiy ia? eiino?oeoeaiee oa?aeoa?.

? ia?aiao?aie, ca aeiiiiiaith yeeo oi?io?oueny naiii?aai?caoe?y
iniiaii? ooieoe?? nenoaie aeeoaiiy – aeinoaaee eenith aei oeaiei ?
aea?ae aoaeaeeneioe, ui ae?iaey?oueny a oeaieiieo ?aca?aoa?ao.

O i?ae?icae?e? 2.8 i?eaaaeaia ? aeine?aeaeaia iaoaiaoe/ia iiaeaeue
o?ainii?oo, ianiiai?io ?ani??aoi?ieo aac?a o i?aai?ci? ethaeeie, ui ?
iae?i?eiith aeeiai?/iith nenoaiith a?aeiinii iai?oaeaiue eenith oa
aoaeaeeneioe a nenoai? e?ia – oeaieii? ?aca?aoa?e

(26)

(27)

, (28)

(29)

– i?iaeia?i a oeaieiao. I?e oeueiio

,

– eiao?oe??ioe.

aecia/athoueny i?e ?ica’ycaii? caaea/? iioeiaeueiiai oi?aae?iiy i?e
ia?aaaaeai? aeeiai?/ii? nenoaie (7)-(10), (26)-( 29) ?c cao?aiiai noaio
a oiiae a?aeiinii? ??aiiaaae i?e yeeo

, (30)

,

– aeineoue iae? aeiaeaoi? aaee/eie.

aecia/a?oueny ii a?aeiioaiith aei e?eoa??th yeino? oi?aae?iiy

(31)

,

– aeiionoeia iiiaeeia oi?aae?iue.

O?ao?e ?icae?e i?enay/aiee ?ic?iaoe? aeai?eoi?a oi?aae?iiy i?ioeanii
ia?aaoaaiiy ethaeeie ia aeeaei? ia an?o eiai noaae?yo – eiii?an??,
aeniiceoe?? ia aeeaei? oa aeaeiii?an??.

?icaeyaea?oueny aeiaaeie, eiee eiii?an?y ? aeniiceoe?y ia aeeaei?
?aaoeththoueny ca aeiiiiiaith i?ia?aiiiai oi?aae?iiy.

O i?ae?icae?e? 3.1 cai?iiiiiaaii aeai?eoi i?iaaaeaiiy eiii?an??, i?e
yeiio oi?aae?iiy i?ioeanii cae?enith?oueny iaia?aae aecia/aieie neeaaeii
aeeoaeueii? noi?o? (a caeaaeiino? a?ae caaeaii? aeeaeie caio?aiiy) oa
oaeaeeino? eiii?an?? ?, aeey iii’yeoaiiy iaaaoeaieo iane?aee?a ae??
a?ia?aa?e/ieo oiia ia i?aai?ci, iiaeooue i?aai?ciaoaaoenue o?eaae?
coieiee i?ioeano aeey ei?aeoe?? noaio i?aai?cio aiaeieaca. Aeai?eoi
i?iaaaeaiiy eiii?an?? caaacia/o? ioe?ieo noaio ia’?eoo oi?aae?iiy
(aecia/a? iai?oaeaiiy ?ia?oieo aac?a o e?ia? ? oeaieiao) ia iiiaio
cae?i/aiiy eiii?an??, oiaoi i?e aeinyaiaii? caaeaii? aeeaeie caio?aiiy.

(ui aecia/a?oueny /a?ac /anoioo na?oeaaeo nei?i/aiue), na?aae i?aai?a
? oeaiei. Oeeie aeaieie ei?aeoo?oueny iiaeaeue ia’?eoo oi?aae?iiy ?
aecia/a?oueny eiai noai a iiiaio cae?i/aiiy aeniiceoe??.

Iaoiae iioeiaeueiiai oi?aae?iiy aacia/iith aeaeiii?an??th aeeeaaea?oueny
o i?ae?icae?e? 3.3. A?i aeeth/a? i?ioeaaeo?e:

ia iiaa?oith ii?y;

, ye? i?i?i?cothoue /an aeaeiii?an??.

Iii?ia aacia/ia o?a?eoi??y aoaeo?oueny ianooiiei /eiii.

). Cia/aiiy iiiaio?a /ano, i?e yeeo ii/eiaeenue i?aeeii o?a?eoi??? ?
coieiee, o?enothoueny, ye ? cia/aiiy iai?oaeaiue ?ia?oieo aac?a o e?ia?
? oeaieiao.

aecia/a?oueny oa?aeoa?ii oa ?ioaineai?noth aeeiioaaii? ?iaioe i?ae /an
noiyiie ia o?a?eoi???.

? i?iaiaeeoueny ?ic?aooiie iiai? iii?ii? o?a?eoi???. I?e oeueiio
e?euee?noue aoai?a i?aeeiio iiaea nei?ioeoenue.

ia ia?oiio aoai? i?aeeiio.

, a oea i?enei?th? i?ioean aeieaaiiy ?ia?oieo aac?a c oeaiei.

I?ae?icae?e 3.5 i?enay/aiee ia/enethaaeueiei aenia?eiaioai c iiaeaeyie,
?ic?aooieo iioeiaeueieo uiaei oaeaeeiae?? ?aaeei?a aacia/ii?
aeaeiii?an?? oa aiae?co ?acoeueoao?a ia/enethaaeueieo aenia?eiaio?a c
iiaeaeeth.

?c cai?iiiiiaaieie o aeena?oaoe?? iaoaiaoe/ieie iiaeaeyie iioeiaeueiiai
uiaei oaeaeeiae?? oi?aae?iiy aacia/iith aeaeiii?an??th i?iaaaeaia na??y
ia/enethaaeueieo aenia?eiaio?a, ?acoeueoaoe yeeo ii??aithaaeenue c
aeaieie i?eaaaeaieie a iiiia?ao?? “Iaaeeoeeineea i?iaeaiu iiaeaiaeiuo
iia?oaeaiee” (i?ae ?aaeaeoe??th I.A.Aaiiaoa ? Ae.A.Aee?ioa, Iineaa,
Iaaeeoeeia,1988) oa a “Aaeeiua i?aaeea io?aiu o?oaea ia aiaeieaciuo
?aaioao” (Iineaa, O?ainii?o,1965). ?acoeueoaoe aenia?eiaio?a na?ae/aoue,
ui cai?iiiiiaai? aeai?eoie oi?aae?iiy aeaeiii?an??th iiaeooue a
caeaaeiino? a?ae oiia, i?e yeeo aiia ?icii/eia?oueny, ciaioeoe
o?eaae?noue aeaeiii?an?? ia 10-25%, ui oa?aeoa?eco? a aeinoaoi?e i???
aoaeoeai?noue aeai?eoio.

INIIAI? ?ACOEUeOAOE ?IAIOE

1. Iiaoaeiaaii, iaa?oioiaaii oa aeine?aeaeaii iaoaiaoe/io iiaeaeue
ianiiai?io oa o?ainii?oo ?ia?oieo aac?a o i?aai?ci? i?e a?ia?aa???.

2. Noi?ioeueiaaia caaea/a oi?aae?iiy aeaeiii?an??th ye caaea/a
iioeiaeueiiai uiaei oaeaeeiae?? oi?aae?iiy aeaeiii?an??th ca ?aooiie
aeai?o neeaaeo aeeoaeueii? noi?o? oa oaeaeeino? i?aeeiio ia o?a?eoi???.

3. ?ic?iaeaii aeai?eoie oi?aae?iiy i?ioeanii caio?aiiy – eiii?an??,
aeniiceoe?? ia a?oio? oa iioeiaeueiiai oi?aae?iiy uiaei oaeaeeiae??
i?ioeanii aeaeiii?an?? ia ae?eyieao o?a?eoi??? i?ae /an noiyiie oa
i?aeeii?a.

4. ?ic?iaeaii oa aeine?aeaeaii iaoaiaoe/io iiaeaeue oi?aae?iiy
ia?aiao?aie naiii?aai?caoe?? nenoaie e?ia – oeaieii? ?aca?aoa?e c iaoith
nei?i/aiiy /ano aeaeiii?an?? i?e aeeaieiaiaeieo caio?aiiyo.

5. Iaea?aeai? ioe?iee o?eaaeino? aoai?a i?aeeiio ? noiyiie ia
o?a?eoi??yo ?ooo, aea aa?aioiaaia aaciaea i?ioeano aeaeiii?an??.

6. I?iaaaeaia ioe?iea aoaeoeaiino? i?ioeano oi?aae?iiy aeaeiii?an?? i?e
ii??aiyii? aeaieo ?aaeueieo oa ia/enethaaeueieo aenia?eiaio?a.

Iniiai? iieiaeaiiy aeena?oaoe?? iioae?eiaai? a oaeeo i?aoeyo:

1. Iiii/oe A.TH., Iieeieaae/ E.A. Iiaeaee?iaaiea aeeiaieee iai?yaeaiee
aacia a i?aaiecia aeaaiaaoa i?e ?aaioa a aeia?aa?e/aneeo oneiaeyo //Na.
iao/i. o?. Oi?aaeaiea e eiiiuethoa?iua oaoiieiaee a aeieiaee e
iaaeeoeeia. Eeaa: Einoeooo eeaa?iaoeee IAI Oe?aeiu. – 1996. – N.62-66.

2 .Iiii/oe A.TH. Iiaeaeue oi?aaeaiey aeaeiii?anneae e a? iaoaiaoe/aneee
aiaeec //Eeaa?iaoeea e nenoaiiue aiaeec. – 1997. – ?2. – N.107-122.

3. Iiii/oe TH.I., Ia?/aiei Ae.?., Iie?ieaae/ E.A., Iiii/oe A.TH. Caaea/?
iioei?caoe?? i?e iiaeaethaaii? ooieoe?e a?inenoai //Ca. iaoe. i?.
Ieoaiiy iioei?caoe?? ia/eneaiue. E.: ?inoeooo e?aa?iaoeee IAI Oe?a?ie. –
1997. – N.239-244.

4. Iiii/oe A.TH. Aeai?eoie/aneia eioi?iaoeeiiiia iaania/aiea i?ioeanna
aeaeiii?annee //Na. iao/. o?. Eioi?iaoeeiiiua oaoiieiaee a aeieiaee e
iaaeeoeeia. Eeaa: Einoeooo eeaa?iaoeee IAI Oe?aeiu. – 1997. – N.51-55.

5. Iiii/oe A.TH. Iaoaiaoe/aneia iiaeaee?iaaiea i?ioeanna eiiiainaoeee
aeiiene/aneeo ninoiyiee i?e aeia?aa?ee //A ei.: A?iien?y: aeano?oeoeaia
oa eiino?oeoeaia ae?y. Iaoa??aee iaoeiai? eiioa?aioe??. Eeaa, 1998. –
N.143-144.

6. Iiii/oe A.TH. Ia iaeiie caaea/a oaeia?iiai oi?aaeaiey i?ioeannii
aaciianuuaiey oeaiae i?aaiecia i?e aeia?aa?ee //Na. iao/. o?. Oai?ey
iioeiaeueiuo ?aoaiee. – Eeaa: Einoeooo eeaa?iaoeee IAI Oe?aeiu. – 1999.
– N.18-22.

Iiii/oe Aaeeia TH???aia. Iaoaiaoe/i? iiaeae? i?ioeano oi?aae?iiy
aeaeiii?an??th oa ?o aiae?c. -?oeiien.

Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.05.02 – iaoaiaoe/ia
iiaeaethaaiiy oa ia/enethaaeuei? iaoiaee. –?inoeooo e?aa?iaoeee ?iai?
A.I.Aeooeiaa IAI Oe?a?ie, Ee?a, 1999.

?icaeyioo? aeooaeuei? ieoaiiy iaoaiaoe/iiai iiaeaethaaiiy i?ioean?a
oi?aae?iiy aacia/iith aeaeiii?an??th. Noi?ioeueiaaia caaea/a
iioeiaeueiiai uiaei oaeaeeiae?? oi?aae?iiy i?ioeanii aaciiane/aiiy
i?aai?cio ?ia?oieie aacaie i?e oaciaeo iaiaaeaiiyo. Aeiaaaeaia
aaeaeaaoi?noue iiaeae? ?aaeueii i?io?eath/ei a i?aai?ci? i?e a?ia?aa???
i?ioeanai. Cai?iiiiiaaii ? iaa?oioiaaii aeai?eoie aeai?o iioeiaeueieo
ia?aiao??a oi?aae?iiy – neeaaeo aeeoaeueii? noi?o? oa oaeaeeino?
aeaeiii?an?? . ?ic?iaeaii iaoiaeeeo oi?aae?iiy ia?aiao?aie
naiii?aai?caoe?? nenoaie ianiia?aiino ?ani??aoi?ieo oa ?ia?oieo aac?a
i?e iiaa?iaii? aeaaiaaoa aei ii?iiaa?e/ieo oiia aeeoo?ae?yeueiino?. Aeey
ioe?iee aoaeoeaiino? aeai?eoi?a i?iaaaeaii na??th ia/enethaaeueieo
aenia?eiaio?a c iaoaiaoe/ieie iiaeaeyie.

Eeth/ia? neiaa: iaoaiaoe/i? iiaeae? ianiiai?io aac?a, iioeiaeueia
oi?aae?iiy uiaei oaeaeeiae??, naiii?aai?caoe?y, aeaeiii?an?y,
a?ia?aa??y, ia/enethaaeuei? aenia?eiaioe.

Iiii/oe Aaeeia TH?ueaaia. Iaoaiaoe/aneea iiaeaee i?ioeanna oi?aaeaiey
aeaeiii?anneae e eo aiaeec. – ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/?iie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.05.02. – iaoaiaoe/aneia
iiaeaee?iaaiea e au/eneeoaeueiua iaoiaeu. – Einoeooo eeaa?iaoeee eiaie
A.I. Aeooeiaa IAI Oe?aeiu, Eeaa, 1999.

?anniio?aiu aeooaeueiua aii?inu iaoaiaoe/aneiai iiaeaee?iaaiey
i?ioeannia oi?aaeaiey aeaeiii?anneae aeaaiaaoa, iiaeaa?aaaoaainy
aicaeaenoaeth iiauoaiiiai aeae?inoaoe/aneiai aeaaeaiey. Iauaeoii
oi?aaeaiey ii?aaeae?i i?ioeann o?ainii?oa e ianniiaiaia eia?oiuo aacia –
acioa e aaeey – a e?iae e oeaiaauo ?aca?aoa?ao i?aaiecia, ninoiyiea
eioi?iai ioeaieaaaony iai?yaeaieai aacia. Iiaeaeue i?ioeanna
i?aaenoaaeaia nenoaiie aeeooa?aioeeaeueiuo o?aaiaiee, eiee/anoai eioi?uo
caaeneo io /enea ?anniao?eaaaiuo oeaiaauo ?aca?aoa?ia. I?aaeiieaaaaony,
/oi i?e eiii?annee e aeaeiii?annee iai?yaeaiea eia?oiuo aacia a
a?oa?eaeueiie e?iae niioaaonoaoao eo ia?oeeaeueiiio aeaaeaieth a
aeuoaoaeueiie niane. I?iaaaeaii enneaaeiaaiea aaeaeaaoiinoe
iaoaiaoe/aneie iiaeaee iauaeoa oi?aaeaiey ?aaeueiui i?ioeannai,
i?ioaeathuei a i?aaiecia i?e aeia?aa?ee..

Caaea/a oi?aaeaiey aeaeiii?anneae noi?ioee?iaaia eae caaea/a ia?aaiaea
aeeiaie/aneie nenoaiu ec ninoiyiey aiciou?iiiai aicaeaenoaeai
aeia?aa?e/aneeo oneiaee a ninoiyiea, niioaaonoaothuaa ii?iiaa?e/aneei
oneiaeyi, ca n/?o auai?a oi?aaeythueo ia?aiao?ia – ninoaaa aeuoaoaeueiie
niane e nei?inoe aeaeiii?annee – ec caaeaiiuo aeiionoeiuo iiiaeanoa.
Aaciianiinoue aeey i?aaiecia i?ioeanna aeaeiii?annee ii?aaeaeyaony
nenoaiie ia?aaainoa, onoaiaaeeaathueo niioiioaiey iaaeaeo iioieaie
eia?oiuo aacia ec oeaiaauo ?aca?aoa?ia a e?iaue eaieeey?ia e iioieaie
niioaaonoaothueo ?anoai??iiuo a e?iae aacia. Nenoaia ia?aaainoa caaea?o
oaciaua ia?aie/aiey ia ?aoaiey caaea/e oi?aaeaiey. Onoaiiaeaii, /oi
nenoaia o?aaiaiee, iienuaathuay aeeiaieeo iai?yaeaiee aacia a i?aaiecia
i?e aeia?aa?ee, oi?aaeyaia. ?aoaiea caaea/e oi?aaeaiey iouneeaaaony a
iiiaeanoaa o?aaeoi?ee, ia eioi?uo yoaiu iiaeu?ia (ia aeoaeia)
/a?aaeothony n yoaiaie noiyiie. Aeaiu ioeaiee i?iaeieaeeoaeueiinoe yoeo
yoaiia e iieacaii, /oi a neo/aa, eiaaea nianue eia?oiuo aacia
aeaooeiiiiiaioiay – i?iaeieaeeoaeueiinoe yoeo yoaiia eiia/iu.

E?eoa?eai iioeiaeueiinoe ii?aaeaeaii a?aiy aeaeiii?annee. ?ac?aaioaiu
aeai?eoiu ?aoaiey caaea/e iioeiaeueiiai ii auno?iaeaenoaeth oi?aaeaiey
aeaeiii?anneae i?e caaeaiiuo oaciauo ia?aie/aieyo. Aeai?eoi aeeth/aao
i?ioeaaeo?o iino?iaiey aaciaie o?aaeoi?ee e niiniaia a? oeo/oaiey ca
n/?o auai?a oi?aaeythueo ia?aiao?ia ec aeene?aoii caaeaiiuo iiiaeanoa.

?anniio?aia iiaeaeue i?ioeanna ianniia?aiina ?anie?aoi?iuo e eia?oiuo
aacia a i?aaiecia i?e aeia?aa?ee e noi?ioee?iaaia caaea/a aai
naiii?aaiecaoeee. ?aoaiea yoie caaea/e naycuaaaony n eciaiaieai
no?oeoo?u iauaeoa oi?aaeaiey a caaea/a iino?iaiey iioeiaeueiuo ?aaeeiia
aeaeiii?annee. Iainiiaaia oeaeaniia?aciinoue auiieiaiey aeiionoeiuo
iaa?ocie ia yoaiao noiyiie, niinianoaothueo oiaiueoaieth a?aiaie
aeaeiii?annee.

I?ia?aiiiay ?aaeecaoeey aeai?eoia oi?aaeaiey aeaeiii?anneae
?anniao?eaaaony eae ninoaaiay /anoue iaoaiaoe/aneiai iaania/aiey
aaoiiaoece?iaaiiiai ?aai/aai ianoa ?oeiaiaeeoaey aiaeieaciuo ?aaio.
Yooaeoeaiinoue aeai?eoiia iiaeoaa?aeaeaaony ?acoeueoaoaie
au/eneeoaeueiuo yenia?eiaioia i?e iiaeaee?iaaiee oaaee/iuo e
yenia?eiaioaeueiuo ?aaeeiia.

Eeth/aaua neiaa: iaoaiaoe/aneea iiaeaee ianniia?aiina aacia,
iioeiaeueiia oi?aaeaiea ii auno?iaeaenoaeth, naiii?aaiecaoeey,
aeaeiii?anney, aeia?aa?ey, au/eneeoaeueiua yenia?eiaiou.

Onopchuk Galina Yuriyivna. Mathematical models of control of
decompression process and their analysis. – Manuscript.

Thesis for degree of Candidate of Science (Ph. D) in Physics and
Mathematics by the speciality 01.05.02. – mathematical modeling and
numerical methods. – V.M. Glushkov Institute of Cybernetics NAS of
Ukraine, Kyiv, 1999.

The dissertation is devoted to the problems of mathematical modeling of
control processes of safe decompression. The problem is formulated as
the problem of optimal control in speed of process of organism
saturation by inert gases by phase restrictions. The adequacy of model
to processes really proceeding in organism by hyperbaria is proved. The
algorithms of a choice of optimal parameters of control – structure of a
respiratory mix and speed of decompression depending on the entry
conditions are offered and proved. The technique of control of
parameters of self-organizing system is developed at aquanaut returning
to normal conditions. For an estimation of efficiency of algorithms a
series of computing experiments with mathematical models is carried out.

Key words: mathematical models of transport of gases, optimal control in
speed, self-organizing, decompression, hyperbaria, computing
experiments.

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